Eliminate the parameter to find the Cartesian equation of the curve, then sketch the curve and indicate with arrows in which direction the curve is traced as the parameter increases: x = e^t , y = e^−2t

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (2, 0,…

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Q: 1. Calculate the moment of inertia about x-axis of the first quadrant portion of the curve: y = 4-…

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Q: Find the equation of tangent plane to this surface at the point where x :1 and y = -1.

A: Given surface is z=f(x,y)=sin(π (3x+2y)) +x2y2 Equation of tangent plane is given by,…

Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: Use Newton’s method to find the coordinates, correct to six decimal places, of the point on the…

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Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: Find the length of curve - Vsec*t-1 dt -<ys=

A: To find- Find the length of curve x = ∫0ysec4t - 1 dt, -π4 ≤ y ≤ π4

Q: Find the arc length of the curve x = -2y³/2 from y = 0 to y = 10. Length =

A: The given curve is x=-2y32 from y=0 to y=10. Find the arc length. As we know the formula of arc…

Q: Q: Find the equation of the tangent plane to the surface:- z-Ln(xj) -x5J , atthe poit (7,4)

A: The given surface is z=lnx2y-xy=fx,y at the point -12, 4. The equation of tangent plane is…

Q: Find the length of the curve y = 4x, 0<y< 2. Arc length =

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Q: Find the points where the line y=−3xy=-3x intersects a circle of radius 2 centered at the origin.…

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Q: Find the arc-length of the curve y = 2x2 +3,0 <x < 1.

A: We can find the arc length as below

Q: Find an equation of the tangent plane to the surface at the given point. 2 x2 + 2z?ey - x = 33, P =…

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Q: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: Find the equation of the tangent line to the parametric curve x = 2t2 and y = 7t2 – 2t3 – 1 at the…

A: find the slope of function using the chain rule and then use the equation  of a tangent line to…

Q: Find the exact length of the curve. 1 y = 1 + cosh(8x), 0 ≤ x ≤ 1 8

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Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t

A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…

Q: Find the slopes of the tangent lines to the ellipse 4x +y = 40 at y=2. The smaller slope is The…

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Q: Find the arc length function for the curve y = 2x3/2 starting at the point (1,2). %3D

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Q: Find the equation of the tangent line to the parametric curve at the indicated point. Show all work.…

A: Equation of tangent line : y - y0 = m ( x - x0 ) m is the slope of tangent line .

Q: Consider the curve x²y + y2x = 6 %3D Find the coordinates of the point (x,y) where the curve has a…

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Q: 1+lnx y =

A: y = 1+ln xx

Q: Find the length of the curve y = ln (sec x), 0 <I<÷.

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Q: Find the Sufface arca 0f the soid of revolution Obtained bu rotatig y=+2x With TtxE2 around メーaxis、…

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Q: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

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Q: Find parametric equations for the tangent line to the curve given by x=ln(t+1), y=tcos2t, z=et at…

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Q: Find parametric equations for the semicircle x2 + y2 = a2, y &gt; 0, using as parameter the slope t…

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Q: Find the slope of then tangent line to the parametric curve t t2 + 25, y 6. at t = -1 and t = 1…

A: Shown below

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(4,0,4) on the…

A: The above problem is solved.

Q: Find the arclength of the curve: y = 5(x + 2)3/2,2 <x<7

A: The arc length is given by, S=∫ab1+f'x2dx   Find the derivative of the function y=5x+23/2.…

Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: At what point is the tangent line to the curve y° = 6x² perpendicular to the line 2x – y – 1 = 0?…

A: Given: y3=6x2..(1)2x-y-1=0y=2x-1...2   As we know that, iI two lines are perpendicular to each other…

Q: Find an equation of the plane tangent to the following surface at the given point. 1 sin (xyz) =

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (4, 0,…

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Q: x = sin´t, y = cosʻt, 0<t<3™

A: Given x=sin2t, y=cos2t, 0≤t≤3π

Q: Find arc length for the curve (y+1)2=4x3 x=0 ,x=1

A: This question can be solved using the concept of length of arc of a given curve over a given…

Q: Find the distance between the point (1,1) and (3,9) along the curve y=x2

A: Given:The points (1,1) and (3,9) along the curve y=x2To find the distance we need use calculus as…

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = = arctan 2, (9,…

A: Follow the procedure given below.

Q: Find an equation of the tangent plane to the given surface at the specified point. 5Vy Z = (-1, 1,…

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Q: Sketch the curve and find the axis. y = Sinx; [0,] 2

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the Surface avea Gevereatel by vevoluing the curve y-2r coso about te x-axis X-Sine

A: According to the given information, it is required to find the surface area generated by revolving…

Q: Q1(b). Find Equations of tangent and normal lines to the curves x = aCos²0.Sin0 & y = bSin²0.Coc0 at…

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Q: Determine the (1) graph, (2) initial and terminal points, (3) orientation, (4) the dy derivative ,…

A: Formula: sin2 t+ cos2 t=1 The given parametric equation is: x(t)=3+ sin(t) and y(t)=-2+ cos(t) where…

Q: Make the curve y = ax4 + bx3 + cx2 + dx + e pass through the points (0,3) and (-2,7) and at (1,4)…

A: The curve y=ax4+bx3+cx2+dx+e

Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: . Determine the points where the curve 6x+ 4y-y=6 has a vertical tangent line. p. Does the curve…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.